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Extreme cases: ionic compounds (LiF)

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A 1. A 1. Li transfers e - to F, forming Li + and F - . This means it occupies a MO centered on the F. Extreme cases: ionic compounds (LiF). orbitals. Molecular orbitals for larger molecules. 1. Determine point group of molecule (if linear, use D 2h and C 2v instead of D ∞h or C ∞v ).

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Presentation Transcript
slide1

A1

A1

Li transfers e- to F, forming Li+ and F-. This means it occupies a MO centered on the F

Extreme cases: ionic compounds (LiF)

orbitals

slide2

Molecular orbitals for larger molecules

1. Determine point group of molecule (if linear, use D2h and C2v instead of D∞h or C∞v)

2. Assign x, y, z coordinates

(z axis is higher rotation axis; if non-linear y axis in outer atoms point to central atom)

3. Find the characters of the reducible representation for the combination of 2s orbitals on the outer atoms, then for px, py, pz. (as for vibrations, orbitals that change position = 0, orbitals that do not change =1; and orbitals that remain in the same position but change sign = -1)

4. Find the irreducible representations (they correspond to the symmetry of group orbitals, also

called Symmetry Adapted Linear Combinations SALC’s of the orbitals).

5. Find AO’s in central atom with the same symmetry

6. Combine AO’s from central atom with those group orbitals of same symmetry and similar E

slide3

F-H-F- D∞h, use D2h

1st consider combinations of

2s and 2p orbitals on F atoms

Obtain the reducible rep based on equivalent F 2s orbitals.

Use Reduction Procedure to get the irreducible reps.

G2s = Ag + B1u

Use the Projection Operator to obtain a SALC for each irreducible rep

Repeat for each group of equivalent atomic orbitals to obtain the full set of eight SALC.

slide4

SALC can now be treated similarly to the atomic orbitals

and combined with appropriate AO’s from H

1s(H) is Ag so it matches two SALC.

The interaction can be bonding or antibonding.

Both interactions are symmetry allowed, how about energies?

slide5

Orbital potential energies (see also Table 5-1 in p. 134 of textbook)

Average energies for all electrons in the same level, e.g., 3p

(use to estimate which orbitals may interact)

slide6

Good E match

Strong interaction

Poor E match

weak interaction

-13.6 eV

-18.65 eV

-40.2 eV

slide7

Characterize the electrons: bonding, non-bonding, antibonding.

Lewis structure

F-H-F-

implies 4 e around H !

MO analysis

defines 3c-2e bond

(2e delocalized over 3 atoms)

Bonding e

Non-bonding e

slide8

CO2

D∞h, use D2h

(O O) group orbitals the same as for (F F)!!

But C has more AO’s to be considered than H !

slide9

No match

CO2

D∞h, use D2h

Carbon orbitals

slide14

Symmetry allows many interactions. Energy considerations guide as to which is important.

Primary B1u interaction

Primary Ag interaction

SALC of Ag and B1u

SALC of Ag and B1u

Strengths of Interactions

Ag :2s(C); -15.9 --- SALC of 2s(O);– 32.4 : D = 16.5

vs

2s(C) ); -19.4 --- SALC of 2p(O); -15.9: D = 3.5

B1u: 2pz(C); -10.7 --- SALC of 2s(O); -32.4: D = 21.7

vs

2pz(C); -10.7 --- SALC 2p(O); -15.9: D = 5.2

slide15

Primary B1u interaction

Primary Ag interaction

slide16

Non-bonding p

Bonding p

4 bonds

All occupied MO’s are 3c-2e

Bonding s

Non-bonding s

slide17

LUMO

The frontier orbitals of CO2

HOMO

slide18

1. Determine point group of molecule: C2v

2. Assign x, y, z coordinates (z axis is higher rotation axis; if non-linear y axis in outer atoms point to central atom - not necessary for H since s orbitals are non-directional)

3. Find the characters of the representation for the combination of 2s orbitals on the outer

atoms, then for px, py, pz. (as for vibrations, orbitals that change position = 0, orbitals

that do not change =1; and orbitals that remain in the same position but change sign = -1)

4. Find the irreducible representations (they correspond to the symmetry of group orbitals,

also called Symmetry Adapted Linear Combinations SALC’s of the orbitals).

5. Find AO’s in central atom with the same symmetry

6. Combine AO’s from central atom with those group orbitals of same symmetry and similar E

Molecular orbitals for larger molecules: H2O

slide19

G

0

2

0

2

For H H group orbitals

G = A1+ B1

E two orbitals unchanged

C2 two orbitals interchanged

sv two orbitals unchanged

sv’ two orbitals interchanged

slide21

antibonding

antibonding

px

non-bonding

pz

py

slightly

bonding

bonding

bonding

a1 sym

b1 sym

b2 sym

slide22

Molecular orbitals for NH3

Find reducible representation for 3H’s

G

0

1

3

Irreducible representations: G = A1 + E

slide24

anti-bonding

anti-bonding

LUMO

pz

Slightly

bonding

HOMO

bonding

bonding

slide25

Acid-base and donor-acceptor chemistry

Hard and soft acids and bases

slide26

Classical concepts

  • Arrhenius:
    • acids form hydrogen ions H+ (hydronium, oxonium H3O+) in aqueous solution
    • bases form hydroxide ions OH- in aqueous solution
    • acid + base  salt + water
    • e.g. HNO3 + KOH  KNO3 + H2O
  • Brønsted-Lowry:
    • acids tend to lose H+
    • bases tend to gain H+
    • acid 1 + base 1  base 1 + acid 2 (conjugate pairs)
    • H3O+ + NO2-  H2O + HNO2
    • NH4+ + NH2-  NH3 + NH3
    • In any solvent, the reaction always favors the formation of the weaker acids or bases

The Lewis concept is more general

and can be interpreted in terms of MO’s

slide27

d+

d-

C

C

C

O

O

O

M

M

Remember

that frontier orbitals

define the chemistry

of a molecule

CO is a s-donor and

a p-acceptor

slide28

adduct

base

acid

Acids and bases (the Lewis concept)

A base is an electron-pair donor

An acid is an electron-pair acceptor

Lewis acid-base adducts involving metal ions

are called coordination compounds (or complexes)

slide30

New LUMO

(non-bonding)

New HOMO

(bonding)

Frontier orbitals and acid-base reactions

The protonation of NH3

(Td)

(C3v)

slide31

In most acid-base reactions HOMO-LUMO combinations

lead to new HOMO-LUMO of the product

But remember that there must be useful overlap (same symmetry)

and similar energies to form new bonding and antibonding orbitals

What reactions take place if energies are very different?

slide32

Frontier orbitals and acid-base reactions

Very different energies like A-B or A-E

no adducts form

Similar energies like A-C or A-D

adducts form

A base has an electron-pair

in a HOMO of suitable symmetry

to interact with the LUMO of the acid

slide34

Bonding e

Non-bonding e

MO diagram derived from atomic orbitals

(using F…….F group orbitals + H orbitals)

slide35

HOMO-LUMO of HF for s interaction

Non-bonding

(no symmetry match)

Non-bonding

(no E match)

But it is also possible from HF + F-

First form HF

slide36

The MO basis for hydrogen bonding

F-H-F-

LUMO

HOMO

HOMO

First take bonding and antibonding combinations.

slide37

Similarly for unsymmetrical B-H-A

Total energy of B-H-A lower than the sum of the energies of reactants

slide38

Good energy match,

strong H-bonding

e.g. CH3COOH + H2O

Poor energy match, little or no H-bonding

e.g. CH4 + H2O

Very poor energy match

no adduct formed

H+ transfer reaction

e.g. HCl + H2O

slide39

Hard and soft acids and bases

Hard acids or bases are small and non-polarizable

Soft acids and bases are larger and more polarizable

Halide ions increase in softness:

fluoride < chloride<bromide<iodide

Hard-hard or soft-soft interactions are stronger (with less soluble salts)

than hard-soft interactions (which tend to be more soluble).

slide40

Most metals are classified as Hard (Class a) acids or acceptors.

Exceptions shown below: acceptors metals in red box are always soft (Class b).

Other metals are soft in low oxidation states and are indicated by symbol.

Solubilities: AgF > AgCl > AgBr >AgI

But…… LiBr > LiCl > LiI > LiF

Class (b) or soft always

slide41

Chatt’s explanationClass (b) soft metals have d electrons available for p-bonding

Model: Base donates electron density to metal acceptor. Back donation, from acid to base, may occur from the d electrons of the acid metal into vacant orbitals on the base.

Higher oxidation states of elements to the right of transition metals have more class b character

since there are electrons outside the d shell.

Ex. (Tl(III) > Tl(I), has two 6s electrons outside the 5d making them less available for π-bonding)

For transition metals:

high oxidation states and position to the left of periodic table are hard

low oxidation states and position to the rightof periodic table are soft

Soft donor molecules or ions that are readily polarizable and have vacant d or π* orbitals

available for π-bonding react best with class (b) soft metals

slide43

Tendency to complex with hard metal ions

N >> P > As > Sb

O >> S > Se > Te

F > Cl > Br > I

Tendency to complex with soft metal ions

N << P > As > Sb

O << S > Se ~ Te

F < Cl < Br < I

slide44

The hard-soft distinction is linked to polarizability, the degree to which a molecule

or ion may be easily distorted by interaction with other molecules or ions.

Hard acids or bases are small and non-polarizable

Soft acids and bases are larger and more polarizable

Hard acids are cations with high positive charge (3+ or greater),

or cations with d electrons not available for π-bonding

Soft acids are cations with a moderate positive charge (2+ or lower),

Or cations with d electrons readily availbale for π-bonding

The larger and more massive an ion, the softer (large number of internal electrons

Shield the outer ones making the atom or ion more polarizable)

For bases, a large number of electrons or a larger size are related to soft character

slide45

Hard acids tend to react better with hard bases and soft acids with soft bases, in order to produce hard-hard or soft-soft combinations

In general, hard-hard combinations are energetically

more favorable than soft-soft

An acid or a base may be hard or soft

and at the same time it may be strong or weak

Both characteristics must always be taken into account

e.g. If two bases equally soft compete for the same acid,

the one with greater basicity will be preferred

but if they are not equally soft, the preference may be inverted

slide46

Fajans’ rules

  • For a given cation, covalent character increases
  • with increasing anion size. F<Cl<Br<I
  • For a given anion, covalent character increases
  • with decreasing cation size. K<Na<Li
  • The covalent character increases
  • with increasing charge on either ion.
  • Covalent character is greater for cations with non-noble gas
  • electronic configurations.

A greater covalent character resulting from a soft-soft interaction is related

to lower solubility, color and short interionic distances,

whereas hard-hard interactions result in colorless and highly soluble compounds

slide48

Quantitative measurements

Absolute hardness

(Pearson)

Mulliken’s absolute electronegativity

(Pearson)

EHOMO = -I

ELUMO = -A

Softness

slide49

Energy levels

  • for halogens
  • and relations between
  • , h and HOMO-LUMO energies
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